Lecture 8

Fundamentals of Physics

Phys 120, Fall 2015

Entropy - the second law of Thermodynamics

A. J. Wagner

North Dakota State University, Fargo, ND 58102

Fargo, September 17, 2015

Overview

• Heat flows to equalize temperatures! The Second Law of Thermodynamics.

• Heat engines

• Energy quality - the arrow of time / entropy

• The automobile - energy consuption

• Transportation efficiency

• The steam-electric power plant

• Exponential growth

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The History of heat

Early Greek Philosophers like Heraclitus (535BC–475BC) assumed that heat is

one of the three elements that everything is made off: earth, water, and fire.

Fire was considered closely related to heat. Heraclitus developed the idea of a

flowing and ever changing world: “You never step into the same river twice.”

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Lucretius c.99c.55 BC

Titus Lucretius Carus) was a Roman poet.

Wrote De Rerum Natura (On the Nature of Things)

Why? Because I teach great truth, and set out to unknotThe mind from the tight strictures of religion, and I writeOf so darkling a subject in a poetry so bright,Nor is my method to no purpose — doctors do as much;Consider a physician with a child who will not sipA disgusting dose of wormwood: first, he coats the goblet’s lipAll round with honey’s sweet blond stickiness, that way to lureGullible youth to taste it, and to drain the bitter cure,The child’s duped but not cheated — rather, put back in the pink-That’s what I do. Since those who’ve never tasted of it thinkThis philosophy’s a bitter pill to swallow, and the throngRecoils, I wished to coat this physic in melliflous song,To kiss it, as it were, with the sweet honey of the Muse.

This treaty on Epicureanism is not the usual Roman way of teaching, rather

it is a unique (and famous) bit of poetry/science teaching.

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Lucretius on random motion of atoms∗

If you should think these atoms have the power to stop and stayAt a standstill, and set new motions going in this way,Then you have rambled far from reason and have gone astray.Since atoms wander through a void, then they must either goCarried along by their own weight or by a random blowInto one another, they bounce apart after the clash(And no surprise, since they are hard and solid, and they lackAnything behind them to obstruct their moving back).

All bodies of matter are in motion. To understand this best,Remember that the atoms do not have a place to rest,And there’s no bottom to the universe, since Space does notHave limits, but is endless. . . .

∗Lucretius, The Nature of Things, Penguin Classics, translated by A.E. Stallings

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Arabic Science of heat

Al-Biruni (973 – 1048), an outstanding Persian scholar from modern day

Afghanistan, is credited with describing the phenomena of getting heat from

motion (through friction):

The earth and the water form one globe, surrounded on all sides by air. Then, sincemuch of the air is in contact with the sphere of the moon, it becomes heated inconsequence of the movement and friction of the parts in contact. Thus there isproduced fire, which surrounds the air, less in amount in the proximity of the polesowing to the slackening of the movement there.

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History of heat

Sir Francis Bacon (1561 – 1626) stated

Heat itself, its essence and quiddity is motion and nothing else.

This idea was, as already hinted at by Lucretius, was developed further by

Daniel Bernoulli (1700–1782) who developed the kinetic theory of gases where

he assumes a particular nature of matter, and explains that temperature is just

the kinetic energy of the particles — and that pressure is just the effect of the

particles collision with the wall.

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Heat engines

It is easy to construct a simple heat

engine. All you need to know is that

gases expand as you heat them and

contract as you cool them.

To build a useful machine you need to

make it work cyclically.

The basic concept then is that you add

a certain amount of heat to your sys-

tem and then you have to remove heat

from your system again.

But how much work can be done using

such a machine?

OriginalTemperature

heat it up −> expansion

The expansion can domechanical work

−>contractioncool down

can also do work!

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What is heat?

In Physics heat is a quantity of energy.

James Prescott Joule (1818–1889) quantified the equivalence of mechanical

work and heat by building a paddle machine that lowered a weight while stirring

a fluid. He could then measure the change in temperature due to the energy

added to the fluid. This he considered a transformation of mechanical energy

to heat energy. (Note that it is easy to transform all the mechanical energy to

heat energy).

Joule postulated that the total energy of a system is conserved (around the

same time as Helmholtz).

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Joule’s energy conservation: 1847 lecture

You see, therefore, that living force (kinetic energy) may be converted into heat, and thatheat may be converted into living force, or its equivalent attraction through space. All threetherefore — namely, heat, living force, and attraction through space (to which I might alsoadd light, were it consistent with the scope of the present lecture) – are mutually convertibleinto one another. In these conversions nothing is lost . . . . We can therefore express theequivalence in definite language applicable at all times and under all circumstances. Thus theattraction of 817 lb. through the space of one foot is equivalent to, and convertible into, theliving force possessed by a body of the same weight of 817 lb. when moving with the velocityof eight feet per second, and this living force is again convertible into the quantity of heatwhich can increase the temperature of one pound of water by one degree Fahrenheit.

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But there is a problem!

While it is easy to transform mechanical energy into heat, the same is not true

for the reverse.

This was noticed much earlier by Sadi Carnot (1796–1832) who wrote an

ingenious paper on the efficiency of heat engines “Reflexions sur la puissance

motrice due feu (Reflections on the Motive power of Fire)” in 1824.

The consequence of this paper was the discovery of the second law of ther-

modynamics. In its own way it is a paper as important as Einstein’s discover

of relativity and the discovery of Quantum Mechanics.

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The second law of thermodynamics

The second law of thermodynamics, stated as the law of heating

Thermal energy flows spontaneously from higher to lower temperature,

but now from lower to higher temperature.

You might think that this is a trivial observation — but we will see that it has

far reaching consequences. This also means that you cannot build a machine

that does nothing else but transfer heat from a cold object to a warmer object.

The first law states that the total energy is conserved.

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Temperature scales

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Concept check

Suppose you put a cold ice-cube in your hand and you observed that the ice-

cube cooled down further while your hand warmed up. This would violate

a) conservation of energy

b) the second law of thermodynamics

c) neither of the above, but other physical laws

d) no known physical laws

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Heat engines: using thermal energy to do work

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How much heat can you transform?

It can’t be all, otherwise I could use that work to heat up a warmer object

violating the second law!

energy efficiency =work output

thermal energy input

The second law of thermodynamics, stated as the law of heat

engines

Any cyclic process that uses thermal energy to do work must also have

a thermal energy exhaust. In other words, heat engines are always less

than 100% efficient at using thermal energy to do work.

Theoretical limit (just a footnote): Eff = (Tin − Tout)/Tin, where temperature is measured inKelvin.

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Efficiencies of heat engines

Engine type Tin(◦C) Tout(

◦C) Max. eff. Act. eff.

Gasoline auto/truck 700 340 37 20Diesel auto/truck 900 340 48 30Steam locomotive 180 100 20 10

Fossil fuel plant 550 40 60 40Nuclear plant 350 40 50 35Solar plant 225 40 40 30Ocean-thermal plant 25 5 7 ???

As you see you get the best efficiency if you burn hot and exhaust cold.

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Concept check

A typical large coal-fired electric-generating plant burns about 1 tonne (1000

kg) of coal every 10 seconds. How much of the tonne goes into producing

electric energy?

(a) 600 kg; (b) 60 kg; (c) 500 kg; (d) 400 kg

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Energy Quality: things run down

Look at a swinging pendulum. It slows down. What happens with the energy?

Can it be recovered?

First law: Energy is conserved

Second law: Energy is degraded to heat

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Entropy

The measure of microscopic disorder is called entropy∗.

The second law of thermodynamics, stated as the law of entropy

The total entropy (or microscopic disorganization) of all the partici-

pants in any physical process cannot decrease during that process, but

it can increase.

This is the underlying reason for the arrow of time (i.e. how the future is

different from the past).

∗We won’t give an exact mathematical definition in this course

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Arrow of time

All microscopic theories (like Newton’s laws) are timereversible, i.e. if you turn

the velocities of all parts of the system around, it will go back to where it came

from. Therefore playing a movie forward and playing it backwards are equally

correct Physics.

But we know that is now true: If I show you a movie of an egg that drops

and breaks, and then show it backwards, you know immediately which version

is forward and which version is backward. But how do you know?

This is because of the law of entropy: in one direction entropy increases (when

the egg breaks) and that is the only way consistent with the second law of

thermodynamics.

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Timeline-600 1920

-100 400 900 1400 1900

Heraclitus Lucretius Al-BiruniBacon

Bernoulli

Newton

Carnot

Helmholtz

Joule

Kelvin

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Summary

• History of Heat

• Heat as motion

• Heat engines

• Entropy

• The arrow of time

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